The open-source Mesa/X.Org developers have been working on LLVMpipe, a Gallium3D driver that accelerates OpenGL and other state trackers on the CPU rather than any GPU driver to provide a better software rasterizer via LLVM optimizations. Unfortunately, it's still slow and can barely keep up with games.

LLVM is only used for code generation - the driver is most likely still compiled with GCC.

GCC is generally slightly faster than LLVM, but it takes at least 10 times as many man-hours to use GCC's backend as it does to use LLVM (and I'm really not exaggerating there).

Also, while GCC might produce slightly faster code, LLVM can do its optimizations and code generation several times faster, which is important for startup speed, when you have to generate an entire OpenGL software renderer plus shaders.